A new fast energy efficient learning algorithm suitable for hardware implemented Kohonen Self-Organizing Map (SOM) is proposed in the paper. The new technique is based on a multistage filtering of the quantization error. The algorithm detects such periods in the learning process, in which the quantization error is decreasing (the ‘activity’ phases), which can be interpreted as a progress in training, as well as the ‘stagnation’ phases, in which the error does not decrease. The neighborhood radius is reduced by 1 always just after the training process enters one of the ‘stagnation’ phases, thus shortening this phase. The comprehensive simulations on the software model (in C++) have been carried out to investigate the influence of the proposed algorithm on the learning process. The learning process has been assessed by the used of five criteria, which allow assessing the learning algorithm in two different ways i.e., by expressing the quality of the vector quantization, as well as the topographic mapping. The new algorithm is able to shorten the overall training process by more than 90% thus reducing the energy consumed by the SOM also by 90%. The proposed training algorithm is to be used in a new high performance Neuroprocessor that will find a broad application in a new generation of Wireless Body Area Networks ( WBAN) used in the monitoring of the biomedical signals like, for example, the Electrocardiogram (ECG) signals.